There are existing methods of obtaining tomographic images of a human body based on the measurement of the spatial distribution of a physical field or radiation that penetrates the object and subsequent reconstruction of the image using the spatial distribution of measured parameters and mathematical methods of convolution and back projection. (The Physics of Medical Imaging. Edited by Steve Webb. Adam Hilger, Bristol and Philadelphia. Chapter 8).
Tomographs, based on the use of x-ray radiation or nuclear magnetic resonance (NMR), are known. (The Physics of Medical Imaging. Edited by Steve Webb. Adam Hilger, Bristol and Philadelphia. Chapter 8).
The known tomographic methods provide high resolution. However, the complicated x-ray or NMR setups used for diagnostics are expensive and difficult in operation, the procedure of inspection is rather long, and the radiation, penetrating a body, is not harmless for patients and operators.
The method of obtaining of a tomographic image of a human body for medical diagnostics, based on the use of electric current, is known as electrical impedance tomography. (Patent of Great Britain 2119520 A, INT CL A61B 5/05, 1983). In the known method a series of contact electrodes is placed on the surface of a patient's body; a source of electric current is connected sequentially to pairs of electrodes; measurements of potential differences (voltages) between pairs of electrodes, arising because of the current flow through the object, are made. Reference values of potential differences are determined based on the assumption of homogeneity of electrical conductivity of the object, or by measuring the same object at different times if the electrical conductivity changes. An image is constructed--from the spatial conductivity distribution of a body or from changes in the conductivity between two measurements--using back projection or the relative differences of measured and reference voltages along equipotential lines of an electric field. It is established that the electrical conductivity of biological tissue depends on its physiological properties. The conductivity distribution of a body can be used to create images of bones, soft tissues and blood vessels.
The electrical impedance tomograph consists of a system of contact electrodes, a unit for electric current excitation, a unit for measurement of potential differences, a microprocessor-based control circuit, a differential amplifier, and analog multiplexers, the inputs of which are connected to contact electrodes and the outputs to the input of the differential amplifier (Patent of Great Britain 2119520 A, INT CL: A61B 5/05, 1983).
However, the use of the method in clinical practice has been hindered until now by the unsolved problem of obtaining absolute or "static" images of satisfactory quality when measurements are carried out on a human body. Existing tomographs allow only dynamic tomograms to be obtained, representing images of conductivity changes between two measurements, which are not informative for medical applications. The inability to visualize static objects is due to the inability to completely solve the inverse problem of the conductivity reconstruction due to the difficulty of obtaining reference values of potential differences when neither the geometry of the boundary surface of the object studied nor the location of measuring electrodes on this surface are known exactly.
Visualization of the absolute conductivity distribution in the cross-section of a human body with a high rate of data acquisition became possible by using a compact tomograph with control of all of its measuring functions by personal computer. The computer carries out processing, visualization and storage of data. (V. A. Cherepenin, A. V. Korjenevsky et al. The Electrical Impedance Tomograph: New Capabilities.//IX International Conference on Electrical Bio-Impedance, Proceedings.--Heidelberg, 1995, p. 430-433). The method of obtaining a tomographic image of a body described in this reference involves: the placing of a series of contact electrodes on the surface of a body; the sequential dipole connection of an electric current source to pairs of adjacent electrodes; the measuring of potential differences between each pair of the rest of the electrodes; the determination of reference values of potential differences; and the reconstruction of the image of spatial distribution of conductivity of a body by back projection of weighted relative differences of the reference and measured voltages along equipotential lines. Reference values of potential differences ##EQU1##
are determined by approximation of the measured distribution of potential differences ##EQU2##
according to the expression: ##EQU3##
Where:
i--the number of exciting pairs of electrodes; PA1 j--the number of measuring pairs of electrodes; ##EQU4## PA1 W.sup.lt, W.sup.rt --weight factors determined according to the procedure of back projection in the direction from the "left" and from the "right" intersection of equipotential lines with the surface of a body, correspondingly, PA1 .SIGMA.--a summation over all positions of the injecting electrodes, ##EQU15## PA1 i--the number of exciting pairs of electrodes, PA1 j--the number of measuring pairs of electrodes, PA1 f.sub.l (j)--given distribution of voltage between adjacent electrodes along the boundary of a reference object, ##EQU17## PA1 W.sup.lt,rt --weight factors, calculated according to the usual procedure of back projection in the direction from the "left" and from the "right" intersections of the equipotential lines with the body's boundary correspondingly, PA1 .SIGMA.--the sum over all positions of the injecting electrodes, ##EQU23##
given distribution of voltage between the adjacent electrodes along the boundary of the reference object; ##EQU5##
signals caused by spurious couplings; and ##EQU6##
approximation coefficients of the measured distribution of potential differences ##EQU7##
In the described solution it is possible to construct a reference data set which does not contain information about the interior structure of the object by using an approximation of the measured data ##EQU8##
by smooth dependencies from a set of simple linearly independent functions. This set, together with an initial set including variations that characterize the interior structure of the object, is used for reconstruction of the absolute conductivity of the object. The measured potential differences can contain considerable systematic errors caused primarily by spurious penetration of signals from channel to channel in the integral multiplexers and input circuits of the tomograph. During the reconstruction of the distribution of spatial conductivity, these noises cause the appearance of artifacts and significantly reduce the quality of the image. To eliminate their influence, a set of spurious signals can be included in the set of base functions used for approximation of the input data. Best results are obtained by using a combination of three functions mentioned in equation (1). The distribution ##EQU9##
is the distribution of voltage between the adjacent electrodes along the boundary of a cylindrical object with homogeneous conductivity when an electric current source is connected to the pair of adjacent electrodes.
The developed algorithm for the reconstruction of the conductivity distribution allows one to obtain medically useful and informative "static" images characterizing the physiological state of organs and tissues. However, the low sensitivity and rather low resolution of this method limits the range of its application.